Location: Cardiovascular Circulation @ feb8451c3889 / Baroreceptor.cellml
- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2020-06-16 17:16:08+12:00
- Desc:
- minor changes
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/4ac/rawfile/feb8451c388983536ab9e20d1752ff3659977da8/Baroreceptor.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="Units.cellml">
<units name="per_s" units_ref="per_s"/>
<units name="per_min" units_ref="per_min"/>
</import>
<units name="Pa_s">
<unit units="pascal"/>
<unit units="second"/>
</units>
<units name="Pa_per_m2">
<unit units="pascal"/>
<unit exponent="-2" units="metre"/>
</units>
<component name="main">
<variable name="t" units="second"/>
<!--// STATE VARIABLES ////-->
<variable initial_value="0.25" name="phi_SN" units="dimensionless"/>
<!-- farction of baroreceptors afferents in firing-permissive states-->
<variable initial_value="0.9" name="s_1" units="dimensionless"/>
<variable initial_value="0.9" name="s_2" units="dimensionless"/>
<!-- aortic diameter-->
<variable initial_value="12.35" name="d_1" units="metre"/>
<!-- cartoid diameter-->
<variable initial_value="12.35" name="d_2" units="metre"/>
<!-- relative dynamic strain-->
<variable initial_value="0.0" name="epsilon_1" units="metre"/>
<variable initial_value="0.0" name="epsilon_2" units="metre"/>
<!-- heart rate-->
<variable name="HR" units="dimensionless"/>
<!-- afferent baroreceptors firing rate-->
<variable name="f_BR1" units="dimensionless"/>
<variable name="f_BR2" units="dimensionless"/>
<!-- baroreceptors saturation-->
<variable name="delta_epsilon_1" units="metre"/>
<variable name="delta_epsilon_2" units="metre"/>
<!-- arterial pressure-->
<variable name="P" units="pascal"/>
<!-- intrathoracic pressure-->
<variable name="P_th" units="pascal"/>
<!--// PARAMETERS ////-->
<!-- vessel wall viscosity parameter-->
<variable initial_value="2.1" name="mu" units="Pa_s"/>
<!-- vessel wall stiffness constant-->
<variable initial_value="0.505" name="k" units="Pa_per_m2"/>
<!-- unstressed wall diameter-->
<variable initial_value="12.35" name="D_1" units="metre"/>
<variable initial_value="12.35" name="D_2" units="metre"/>
<!-- reference diameter-->
<variable initial_value="20.0" name="D_ref" units="metre"/>
<!-- resetting time-->
<variable initial_value="30" name="tau_s" units="second"/>
<!-- saturation constant-->
<variable initial_value="0.4965" name="delta_epsilon_0" units="dimensionless"/>
<!-- afferent fiber activation rate-->
<variable initial_value="0.0651" name="a" units="per_s"/>
<!-- afferent fiber deactivation rate-->
<variable initial_value="0.2004" name="b" units="per_s"/>
<!-- afferent firing rate-->
<variable initial_value="300" name="f_0" units="per_s"/>
<!-- heart rate parameter-->
<variable initial_value="28" name="H_0" units="per_s"/>
<!-- heart rate parameter-->
<variable initial_value="156" name="H_1" units="per_s"/>
<!-- sympathetic tone activation rate-->
<variable initial_value="0.05" name="f_SN" units="per_s"/>
<!-- sympathetic tone inhibition rate-->
<variable initial_value="100" name="f_1" units="dimensionless"/>
<!-- relative aortic-carotid strength-->
<variable initial_value="0.54" name="g" units="dimensionless"/>
<!--// EQUATIONS ////-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_th</ci>
<piecewise>
<piece>
<cn cellml:units="pascal">0</cn>
<apply>
<leq/>
<ci>t</ci>
<cn cellml:units="second">30</cn>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">38</cn>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>t</ci>
<cn cellml:units="second">30</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>t</ci>
<cn cellml:units="second">30</cn>
</apply>
<apply>
<leq/>
<ci>t</ci>
<cn cellml:units="second">49</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">38</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>t</ci>
<cn cellml:units="second">49</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci>t</ci>
<cn cellml:units="second">49</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>HR</ci>
<apply>
<plus/>
<ci>H_0</ci>
<apply>
<times/>
<ci>H_1</ci>
<ci>phi_SN</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>phi_SN</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>f_SN</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>phi_SN</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>f_1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>g</ci>
<ci>f_BR1</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>g</ci>
</apply>
<ci>f_BR2</ci>
</apply>
</apply>
<ci>phi_SN</ci>
</apply>
</apply>
</apply>
<!-- baroreceptor firing rate-->
<apply>
<eq/>
<ci>f_BR1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_0</ci>
<ci>s_1</ci>
<ci>delta_epsilon_1</ci>
</apply>
<apply>
<plus/>
<ci>delta_epsilon_1</ci>
<ci>delta_epsilon_0</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_BR2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_0</ci>
<ci>s_2</ci>
<ci>delta_epsilon_2</ci>
</apply>
<apply>
<plus/>
<ci>delta_epsilon_2</ci>
<ci>delta_epsilon_0</ci>
</apply>
</apply>
</apply>
<!-- baroreceptor activity-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>s_1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>s_1</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>b</ci>
<ci>s_1</ci>
<ci>delta_epsilon_1</ci>
</apply>
<apply>
<plus/>
<ci>delta_epsilon_1</ci>
<ci>delta_epsilon_0</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>s_2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>s_2</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>b</ci>
<ci>s_2</ci>
<ci>delta_epsilon_2</ci>
</apply>
<apply>
<plus/>
<ci>delta_epsilon_2</ci>
<ci>delta_epsilon_0</ci>
</apply>
</apply>
</apply>
</apply>
<!-- relative wall strain-->
<apply>
<eq/>
<ci>delta_epsilon_1</ci>
<apply>
<max/>
<apply>
<minus/>
<ci>d_1</ci>
<ci>epsilon_1</ci>
</apply>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_epsilon_2</ci>
<apply>
<max/>
<apply>
<minus/>
<ci>d_2</ci>
<ci>epsilon_2</ci>
</apply>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
<!-- relative strain-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>epsilon_1</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_1</ci>
<ci>epsilon_1</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>epsilon_2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_2</ci>
<ci>epsilon_2</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
<!-- pressure-diameter relation-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>d_1</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>d_1</ci>
<apply>
<minus/>
<ci>P</ci>
<ci>P_th</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>k</ci>
<ci>d_1</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>d_1</ci>
<ci>D_1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>mu</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>d_2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>d_2</ci>
<ci>P</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>k</ci>
<ci>d_2</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>d_2</ci>
<ci>D_2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>mu</ci>
</apply>
</apply>
<!-- pressure-->
<apply>
<eq/>
<ci>P</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">20</cn>
<apply>
<sin/>
<ci>t</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">100</cn>
</apply>
</apply>
</math>
</component>
</model>